The new dwarf, thornless, primocane-fruiting cultivar of blackberry called ‘APF-236T’ is described herein. The new cultivar originated from a hand-pollinated cross of Arkansas selection A-120T (unpatented selection)×APF-132T (unpatented selection) made in 2007. The seeds resulting from this controlled hybridization were germinated in a greenhouse in the spring of 2008 and planted in a field near Clarksville, Ark. (West-Central Arkansas). The seedlings fruited in the summer of 2009, and one seedling, designated APF-236T, was selected for its thornless canes, very dwarf growth habit, medium-large fruit, good fruit quality, and excellent primocane flower bud formation.